Eleanor D. Campbell

Confidence Interval about the Response at the Stationary Point of a Response Surface, with an Application to Preclinical Cancer Therapy

A method of calculating a confidence interval about the response at the stationary point of a response surface is presented. We show that the technique can also be used to calculate a confidence region about the location of the stationary point. The procedure is applied, via Coxs proportional-hazards model, to the analysis of survival data from a preclinical cancer chemotherapy experiment involving the combination of two drugs. It is seen that the results can be useful in determining the existence of a therapeutic synergism.

An Asymptotic Confidence Region for the ED 100p From the Logistic Response Surface for a Combination of Agents

When viewed in light of the simplicity of the solution in a single variable, it is not surprising that the estimation of the ED10op in combinations has received little attention in the statistical literature. As a result of the increasing interest in the effects of combinations of agents either as the result of treatment or environmental exposure, however, consideration of the estimation of the ED1oop in combinations is warranted. [Skarin, Canellos, Rosenthal, Case, Maclntyre, Pinkus, Moloney, and Frei (1983) reported on the use of a combination of six drugs in the treatment of lymphoma, and Lang, Kurzepa, Cole, and Loper (1980) indicated that several known or suspected carcinogens were identified among the many compounds present in drinking water.] Confidence bands on the logistic response curve were considered by Hauck (1983) and Brand, Pinnock, and Jackson (1973). One of the advantages claimed by Hauck is that his method is not restricted to a single explanatory variable, as is the approach taken by Brand et al. In their paper, however, Brand et al. discussed placing confidence bands about points on the inverse response curve, for example, the ED1oop, a topic not discussed by Hauck. It is the purpose of this article to develop and illustrate a method for estimating a large sample confidence region about the ED1oOP from the logistic curve in the case of multiple explanatory variables. 2. BACKGROUND

Relationships between various uses of antineoplastic drug-interaction terms

SummaryIn in vitro testing, no pharmacologic synergism has been found for the combination of cisplatin and etoposide in P388 leukemia in contrast to the demonstration of therapeutic synergism in the same model. No pharmacologic synergism has been found for the same combination in the treatment of four small-cell lung-cancer cell lines, although clinical results obtained using this combination in small-cell lung cancer and other cancers suggest a therapeutic advantage. The popular concept of synergy, implying a therapeutic advantage, is different from the pharmacologic meaning, which generally implies that less drug is required in a combination for an equal effect. Therapeutic advantage may be obtained regardless of whether drugs are synergistic in the pharmacologic sense in the treatment of a tumor. To gain a more comprehensive insight into concepts of drug interaction, it is important to recognize that the type of drug interaction seen is dependent on the drug doses used and may vary with the treatment of different cell lines. All of these factors complicate the use of the word synergism, or any associated term, in a categorical manner to describe the effects of combinations of antineoplastic drugs.

Assessing the efficacy of azaprophen and physostigmine as a pretreatment for soman-induced incapacitation in guinea pigs by response-surface modeling

Physostigmine (PHY) has the advantage over pyridostigmine of minimizing OP-induced incapacitation because it penetrates into the CNS. However, physostigmine is behaviorally toxic at relatively low concentrations. It is anticipated that this could be offset by a cholinolytic to prevent behavioral deficit due to the carbamate pretreatment alone. The therapeutic efficacy of physostigmine/azaprophen pretreatment therapy was evaluated in soman-challenged guinea pigs. Response surface methodology was employed to describe the relationship of the pretreatment combination with duration of incapacitation. The significance of the combination relative to PHY alone was evaluated in addition to dose combinations that yield optimal time to recovery. Analysis of the fitted response surface indicated that combination pretreatment with these compounds significantly reduces the time to recovery after soman challenge versus pretreatment with PHY alone.

Combination of 5-fluorouracil and cyclophosphamide in L1210 and P388 leukemias with changes in optimum treatments as a function of the age of the L1210 tumor at first treatment.

The interaction of 5-fluorouracil and cyclophosphamide in the treatment of L1210 and P388 leukemias was studied using response surface methodology. Single dose treatment of each drug was administered simultaneously or with a 24-hr interval between 5-fluorouracil and cyclophosphamide to the advanced tumors or at various times after L1210 inoculation. While at low doses the action of the combination of the two drugs was greater than expected, there was no therapeutic synergism if the drugs were given together (optimum doses cyclophosphamide 366 mg/kg and 364 mg/kg, respectively, in advanced L1210 and P388 leukemias) or in the early tumor when cyclophosphamide was given 24 hours after 5-fluorouracil. In the advanced tumor, using the regimen employing a 24-hr interval between drugs, therapeutic synergism could be demonstrated (optimum doses 5-fluorouracil 130 mg/kg followed by cyclophosphamide 248 mg/kg in advanced L1210 leukemia and 5-fluorouracil 110 mg/kg followed by cyclophosphamide 263 mg/kg in advanced P388 leukemia). The evidence generated suggested that improved therapy could be found in two separate regions of the treatment space, raising the possibility of more than one mechanism of drug interaction. The location of the optimal treatment depended on the tumor burden at the time treatment was initiated. A shift from one region to the other occurred after 4-6 days of tumor growth when the original inoculum was 10(5) i.p. L1210 cells. Another more obvious conclusion that can be drawn is that treatment was less effective as the tumor became more advanced. The notion that different tumor stages may require different ratios of drugs in a clinically useful combination should receive attention.

Application of response-surface methodology to detect interactions of genotoxic agents in cultured mammalian cells.

Response-surface methodology (RSM) techniques provide a useful statistical approach for the design and analysis of experiments involving multiple variables. Although it has been used for some time in the areas of chemical engineering and agriculture, RSM has only recently been applied to the solution of biological problems. Here we have utilized RSM to investigate the interaction of two direct-acting, monofunctional alkylating agents [ethyl methanesulfonate (EMS) and ethylnitrosourea (ENU)] in Chinese hamster V79 cells with respect to the in vitro induction of sister chromatid exchanges (SCEs). A factorial design was employed in which the cells were exposed to the agents singly and in simultaneous combinations for 4 h. The cells were collected for SCE determination 30 h after treatment. The analysis revealed concentration-dependent increases in SCEs for both of the agents, with ENU being the more effective on an equimolar basis. In addition, single- and multiple-agent interactions were detected. The most important finding was that over the treatment range studied, a significant negative interaction occurs between EMS and ENU with regard to SCE induction. It is suggested that RSM not only may be useful in determining the statistical relevance of experimental variables but also may generate hypotheses the evaluation of which could provide additional insights into the underlying mechanisms involved.

A Biometric Theory of Middle and Long Distance Track Records

It has been often observed that a plot of average velocity againist distanice or time for world track records suggests a continuous monotonic underlying relationship. Several attempts to discern the nature of this relationship empirically by seeking linearizing transformations have been made with varying degrees of success. The purposes of this paper are to describe an attempt to explain the observed curve by a biometric theory alnd to consider the problem of estimating unkniown parameters occurring in the theory. The theory is applied to world record data of 1959 and records which are below par are pointed out. The development is based on the work of A. V. Hill [1927].

An asymptotic confidence interval for the response at the stationary point of a quadratic response surface

The delta method is utilized to construct an asymptotic 100(1 - alpha)% confidence interval for the response at the stationary point of a quadratic response surface. The end-points of the interval can be found directly, compared to other more, computationally intense procedures that result in a conservative interval. The coverage probability associated with intervals constructed in this manner from studies with relatively small numbers of observations is investigated via a simulation study. Finally, the methodology is illustrated with an example involving the evaluation of a combination of cytotoxic agents in the treatment of murine L1210 leukemia.

A method for determining schedule dependency in tissue culture

A dual-exposure drug treatment of cell lines in tissue culture provides a possible method for determining schedule dependency. This is suggested by results of treatment of human small cell lung carcinoma NIH H209 and murine L1210 leukemia cell lines with cisplatin, a non-schedule-dependent drug, and etoposide, a schedule-dependent drug. Nonlinear least squares was used to estimate the dose-response surface. The estimated regression coefficients for the effect of the first dose compared to that of the second dose support the premise that cisplatin is not schedule dependent. Unlike cisplatin, the second dose of etoposide was shown to be more effective than the first dose in the human small cell carcinoma line. This agrees with known clinical results where multiple etoposide dosing has been shown to be more effective and confirms schedule dependency. This methodology, or a refinement, may offer another tool for studying schedule dependency of drugs using tissue culture methods.